Using an apple corer, core each zucchini, taking care not to pierce the skin (reserve the cores for side dish). Saute the onion in half in olive oil until wilted, then cool.

Soak the bread in the broth for 10 minutes, squeeze dry and combine with lamb, onion, egg, parsley, salt, pepper, a pinch of cayenne and a little freshly grated nutmeg in a bowl; knead well with fingers until combined well. Stuff each zucchini with a little of the lamb filling.

Heat the remaining olive oil in a deep, wide pan (at least 12" deep). Add the zucchini, 1/2 cup of water, sugar, salt and pepper. Cover with an upside-down plate. Cover with a lid and bring to a boil, then simmer for 40 minutes. Remove the lid and the plate, and reduce the liquid in the pan. Serve immediately.

This dish is excellent with a little bit of freshly squeezed lemon juice added at the end. However, for Rosh Hashanah sour flavors are typically avoided since it is a sweet holiday.